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4 Risk measures, appetite and limits

4 Risk measures, appetite and limits

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28



ECONOMIC CAPITAL AND FINANCIAL RISK MANAGEMENT



consider VAR to be a genuine risk measure as it is a well defined quantitative measure of the potential loss that a firm may incur as a result of

accepting a specific type of risk.

In practice however, many firms may not actually measure the risks

that they are taking on. For example, the retail credit risk that is taken on

with a mortgage is often controlled using portfolio limits. Therefore, for

example, firms might put a limit on the proportion of high loan to value

(LTV) business that they are prepared to accept. Although this undoubtedly

allows the firm to control, or limit, credit concentration risk, it does not

measure, or quantify, the amount of risk that is being taken on.

Similarly, mortgage retail banks may measure and monitor arrears

rates by customer segment, for example, the proportion of mortgages

that are three or more payments in arrears, and track these over time. We

would again argue that, although such arrears rates do give an indication

of the amount of relative risk that the firm is running, such measures do

not identify how much absolute risk the firm is running. For example,

arrears rates cannot tell the firm how much money it may lose over

the next 12 months, with a prescribed probability, from the credit risks

associated with mortgages.

Similar points can be made across all risk types.

Generally speaking, for the purposes of this book, we consider that for

a risk measure to be meaningful, it must be capable of quantifying the

potential loss that may result to the firm, over a prescribed time period

and with a prescribed confidence level, or probability, from taking that

risk. Economic capital, described later in this book, is a prime candidate

for such a risk measure as it is capable of handling most, if not all, risks.



3.4.2



Risk appetite



Once a firm has developed a meaningful risk measure for the risks it is

collecting, it is then in a position to specify or articulate its risk appetite,

relative to the risk measure. If a firm does not measure risk in a meaningful way, it is not likely that it will be able to articulate an appetite.

That does not mean to say that it cannot limit or control risk. It can

still set risk limits which will, indeed, control risk, but the firm will not

be able to say anything meaningful about the potential losses that it may

incur as a result of accepting risk.

Note that firm appetite can be set, first, for each risk individually and,

second, for all risks in aggregate. The aggregate appetite may allow for

the potential interactions, or more loosely the potential correlations,

between the risks and may, as a consequence, be less than the sum of the

individual risk appetites. For example, credit risk may tend to be “low”

when market risk is “high”, and so on.



RISK GOVERNANCE



3.4.3



29



Risk limits



Once a firm has articulated its risk appetite, it is then in a position to set

the risk limits that will control risk and keep the collected risks within

the firm’s articulated appetites. For example, the firm might set a trigger

limit at 95% of its articulated appetite to identify when the firm is getting

close to its appetite. As mentioned above, firms may often jump straight

to the limit setting stage, before they have developed meaningful risk

measures and have articulated their risk appetite.

The risk limit should be stated by reference to the underlying risk

measure and will be designed to ensure that the firm stays within its

articulated appetite. For example, if market risk is being measured using

VAR, the limit may be specified by putting an upper limit on a business

unit’s daily VAR, which keeps the firm within its appetite.

Figure 3.4 illustrates this process using our risk control cycle management tool.

The firm begins by measuring the amount of risk it is taking. It then

articulates its appetite relative to the measured amount of risk and,

finally, sets limits, also relative to its risk measure, to ensure that it stays



Measure the risk



Set risk limits



Set risk appetite



Figure 3.4 Risk control cycle



Measure the risk



Set risk limits



Figure 3.5 Risk limit control cycle



Set risk appetite



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ECONOMIC CAPITAL AND FINANCIAL RISK MANAGEMENT



within its articulated appetite. Risk will be measured on a regular and

ongoing basis with risk appetites and risk limits refreshed by the firm,

usually on an annual basis.

Figure 3.5 illustrates the alternative process that some firms may,

however, follow. They start with risk limits and then use those to articulate

their appetite without ever having measured the underlying risk in the

first place.



3.5



R E L AT E C A P I TA L TO R I S K



Under Basel 2, for banks, and new regulations for UK insurers, see

Chapter 14, financial services firms are required to self assess the

amount of capital that they believe is needed to cover the risks they

are running. The level of prescription around how firms should carry

out such a self assessment is, in practice, and by regulatory design,

limited.

However, within the financial services industry, the generally

accepted approach to carrying out this risk capital self assessment is by

using economic capital models of the firm’s business. Economic capital is the main theme of this book and is discussed in full detail in

Chapter 5.

Once a firm has developed the infrastructure and tools required to

determine its self assessed risk capital, firms will be expected and

required to use this risk capital to manage their businesses as follows:

᭿



To ensure that the firm has enough current available capital to

cover the risks it is running, as measured by its current level of risk

capital.



᭿



To ensure that the firm will have enough future available capital to

cover the risks that it is planning to run, as measured by its projected

future risk capital levels. Moreover, the firm should allow for planned

changes in the firm’s risk profile going forward in projecting risk

capital.



᭿



To articulate its risk capital goals explicitly in its strategic and

business plans.



We believe that risk capital is the key risk management tool that all firms

should be using to manage their businesses from a risk perspective.

For example, as mentioned earlier, risk capital could be the fundamental

risk measure used in a firm’s risk control cycle.



RISK GOVERNANCE



3.6



31



REPORTING PROCESSES



3.6.1 Internal reporting

Basel 2 requires that the board of the bank should receive regular reports

on the firm’s risk profile and its risk capital needs. This is mainly to

assess and check that

᭿



Emerging trends in the material risks collected by the firm are being

monitored.



᭿



The assumptions underlying the risk capital calculation are still

appropriate.



᭿



Available capital is sufficient to cover the risks currently being run

by the firm.



᭿



Projected available capital is adequate to cover the risks projected to

be run by the firm.



᭿



The firm’s articulated risk capital goals are still appropriate.



Firms will need to consider how frequently their board should receive

such reports, how detailed the reports should be and in what form they

should be presented. This will tend to be firm specific, driven mainly by

the requirements of the firm’s board and senior managers.

Group board



Group enterprise wide risk



Group risk committees



Firm board



Enterprise wide risk



Risk commitees



Risk units



Figure 3.6 Internal risk reporting process



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ECONOMIC CAPITAL AND FINANCIAL RISK MANAGEMENT



The Pillar 2 type risks and the risk capital calculation tend to cut

across all risk committees and some areas of Finance, such as product

pricing. Firms will therefore need to be very clear in defining the roles

and responsibilities of the various parties involved in preparing the

firm’s internal risk reports.

Consistency with group reporting will also need to be considered as

well as whether the firm’s enterprise wide risk profile, or individual risk

profiles, should be reported to the group centre. The group’s requirements

will be the main driver of this, however.

Figure 3.6 sets out a potential reporting process for a firm that is a part

of a larger financial services group.

In this potential reporting process, the firm’s enterprise wide risk

profile is reported into the group.



3.6.2 External reporting

For external reporting, firms will usually be most concerned to ensure

that they are compliant with the disclosure regulations, that their approach

is consistent with their peers and that it satisfies the needs of all of stakeholders, including investors.

Usually, a board approved disclosure policy will be required by the regulators. This should cover how the specific disclosures were decided upon,

internal controls over the disclosure process and the process for assessing

and monitoring the ongoing appropriateness of the disclosures.

Regulators would also tend to require that disclosures are consistent

with the way that the firm assesses and manages risk. Notwithstanding

all of these points, a firm’s external reporting will, of course, be driven

to a very large extent by its accounting requirements.



3.7



INDEPENDENT REVIEWS OF

I N T E R N A L CO N T R O L S



At least under the Basel 2 banking rules, a firm’s board is responsible for

᭿



The establishment of a process to monitor compliance with internal

policies.



᭿



Verifying that the firm’s internal controls are adequate.



᭿



Periodically reviewing risk management processes.



In practice, firms are likely to handle these requirements by

᭿



Using external consultants to carry out periodic one off reviews to

identify process and control weaknesses.



RISK GOVERNANCE



᭿



33



Relying on the firm’s Audit Committee and both internal and

external auditors to monitor compliance thereafter.



Particular issues that firms may face include:

᭿



There is a limited supply of experienced consultants available in the

market to carry out the one off reviews. Fees therefore tend to be

high and the same advice may sometimes end up being passed

around the industry.



᭿



Many of the consultants are ex-regulators, sometimes with limited

business experience. Firms may therefore receive advice that helps

them comply with the letter of the regulations, but which may not

add much value from a practical risk management perspective.



᭿



Internal audit staff may not be appropriately skilled, nor have

the business experience, to handle the increasingly complex and

challenging risk management requirements that they are being asked

to audit.



3.8



SUMMARY



In this chapter, we have discussed the formal governance structures that

firms are required to put in place to manage the risks they collect. Even if

a firm has put in place its hard, quantitative risk management tools, without the softer, more qualitative risk management tools described in this

chapter, a firm would not be following best risk management practice.

We now move on to consider the fundamentally important topic of

risk measurement in the next chapter.



CHAPTER 4



Stress Testing to

Measure Risk



4.1



INTRODUCTION



As described in Chapter 3, firms are required to self assess the amount of

capital that they believe is needed to cover the risks they are running.

There are many ways in which this self assessment may be carried out

and it will certainly vary across firms.

In this book, we will achieve the self assessment by subjecting the

realistic balance sheet of a firm’s businesses to deterministic stresses or

stochastic stresses. The amount of capital that is required for this realistic

balance sheet to remain solvent, following a range of stresses, then represents the firm’s self assessed risk capital amount. This is described in

more detail in Chapter 5, which deals with economic capital.

Note that, throughout this book, we use this self assessed risk capital

amount as our key measure of risk.

In this chapter, we now define and discuss both deterministic and

stochastic stress testing and compare their relative merits. We first describe

what we mean by a deterministic stress.



4.2



DETERMINISTIC STRESSES



Under a deterministic stress of a firm’s realistic balance sheet, the behavior

of the balance sheet is examined when one, or more, of the firm’s risk

variables are assigned specific extreme values. Although a probability is

sometimes assigned to a deterministic stress, giving a half way house

between deterministic and stochastic stress testing, this tends to be the

exception rather than the norm.

34



STRESS TESTING TO MEASURE RISK



35



Take a retail mortgage bank, for example. The risk capital of the

bank’s mortgage book depends on the future interest rate margin that

the bank may earn on its mortgages. This is the rate of interest earned by

the firm on its mortgages, less the cost of funding these mortgages. The

bank may believe that its average interest rate margin over the lifetime of

its existing in force business is 0.012 p.a.

If everything goes by plan, the bank should earn a margin close to

0.012. If not, it will earn a margin less than 0.012 and capital will be

required to absorb this loss. If the bank does better than planned, its

margin will exceed 0.012 and capital will be released.

The extent to which the margin might be either more, or less, than

0.012 will depend on the specific circumstances of the bank, for example

its funding mix and how stable this is likely to be going forward. The

cost of the bank’s funding will not be known with certainty and will vary

according to both internal influences, for example the bank’s credit

rating, and external influences, for example the credit cycle.

Substantial judgment will, therefore, be required in choosing the

deterministic stresses to be used. Stresses plus, or minus, 25 basis points,

or 0.0025, may be appropriate for one bank, but may be too extreme for

another bank’s management.

Once a full range of deterministic stresses has been designed and

agreed, the realistic balance sheet of the bank’s business is subjected to

each stress and the amount of capital that is required to back the risks

that define each of the deterministic stresses can be calculated.



4.3



S TO C H A S T I C S T R E S S E S



Most, although not all, of the risks that firms collect can be modeled as

random variables, in the formal mathematical statistical sense. Some

examples are given below.



Retail mortgage bank example

As we discussed in Section 4.2, a bank’s margin will usually not

be known with absolute certainty. Modeling this future margin as a

stochastic process allows this uncertainty to be quantified, so assisting

the firm in controlling and managing it. For example, treating the margin

as a stochastic process allows us to quantify how extreme the margin can

be in the tails of its distribution.

Examining the percentiles of the firm’s observed monthly interest rate

margin over a specified period of time will allow the firm to understand



36



ECONOMIC CAPITAL AND FINANCIAL RISK MANAGEMENT



how low its margin can fall to, at each percentile level. Stochastic

models can be designed to replicate this tail behavior and can then be

used by the firm to self assess the amount of risk capital it needs to cover

this type of risk event.



Life insurance annuity example

The capital management of a life insurance firm’s annuity portfolio

depends on the future mortality experience of the firm’s annuitants.

For example, the lighter that its mortality experience is, the greater its

reserves should be to cover liabilities. Most firms’ annuity portfolios are

large enough for current annuitant mortality, across the entire portfolio,

to be stable and estimable with a high degree of accuracy. The biggest

uncertainty, however, is the rate at which mortality will improve in the

future.

Actuaries have consistently underestimated mortality improvement

rates and ongoing advances in medical sciences and genetics may

mean that this improvement rate may even accelerate in future.

Estimating the effect and timing of medical advances on future mortality

is obviously impossible. Nevertheless, it is still feasible to build

simple and credible stochastic models of mortality improvement rates,

based to some extent on what has happened in the past, and these

are useful in quantifying the risks associated with improving future

mortality.



With profits life insurance example

The capital management of regular premium life insurance products

depends on the investment returns that future premiums will earn.

For savings products, this will usually mean the future returns that can

be earned on investment in a mixture of equities and fixed interest assets.

These future returns are obviously not known with certainty.

One approach to handling this uncertainty is to model the returns as

realizations of a specific stochastic process, for example, a multivariate

time series model. Once a credible stochastic model has been developed

and built, future asset returns can be repeatedly simulated using the

model. These returns can then be used to help understand the behavior of

the firm under the stochastic variability, or volatility, captured by the

model. For example, light can be shed on how much risk capital is

required to back the investment guarantees implicit in life insurance with

profits funds. Practical examples illustrating this approach are given in

Chapter 11.



STRESS TESTING TO MEASURE RISK



37



Pension fund example

The amount of funding needed by an occupational pension scheme fund

to meet it liabilities depends on the future fixed unit expenses of the

fund, its ongoing annual maintenance expenses, for example. Future unit

expenses are unknown and, moreover, they depend on numerous factors

that cannot realistically be modeled.

For example, the effectiveness of the fund trustees and the managers

in controlling costs and the absolute size of the fund itself will affect

the fund’s unit expenses. So, it will usually not be practicable, or realistic,

to model the future unit expenses, per se, using a stochastic process. An

alternative approach is to model the rate of increase of unit expenses

from one year to the next.

Over the longer term, this rate of increase will usually be highly

correlated with RPI. For example, if the unit costs are mainly attributable to fixed staff expenses, based on past experience, the rate of increase

of the unit expenses over the longer term is likely to be well modeled

by assuming that it equals RPI plus an additional 1 or 2% p.a. Most

financial services firms have fairly well developed stochastic models of

future RPI.

The examples described above form a very small selection of the type

of risk variables that are amenable to stochastic modeling.



4.4



M U LT I VA R I AT E N AT U R E O F T H E R I S K

VA R I A B L E S



As discussed in Chapter 2, the range of risks that financial services firms

collect is very extensive. For example, even a relatively simple building

society is subject to persistency, expense, HPI, credit, interest rate, liquidity

and operational risks.

It is relatively straightforward to quantify risks individually. However,

in reality risks occur simultaneously, and according to the likelihood of

their mutual occurrences. For example, one might expect poor credit

experience and high interest rates to be dependent, or positively correlated. Likewise, high levels of credit defaults and low, or even negative

HPI, tend to occur when interest rates are high.

For stochastic stresses, therefore, the stochastic process that models

the mutual behaviors of the risk variables that quantify risk will be a

multivariate process. In other words, the model should be capable of

describing risk variable dependencies, as well as the marginal behaviors

of the risk variables themselves. With mortgages, for example, persistency and interest rates may tend to be negatively correlated as customers



38



ECONOMIC CAPITAL AND FINANCIAL RISK MANAGEMENT



may churn their mortgages more in a high interest rate environment.

The stochastic process chosen will therefore need to be able to model

this type of dependency.

For deterministic stresses, the values that particular risk variables take

under the individual stresses will need to be chosen quite judiciously.

For example, in the mortgage example above, the high interest rate

stresses should only contain “low” values for the persistency risk variable.

Given the very large number of risk variables that a financial services

firm is affected by, the dimensionality of the stochastic process used for

stochastic stress testing, and also of the deterministic stresses, will often

be very high. The dimension reduction techniques that are available

for stochastic processes, and their deterministic stress equivalents, will

therefore be of great assistance. In Chapter 7, we develop a high dimensional stochastic model that is built up from relatively low dimensional

building blocks.



4.5



C AU S A L N AT U R E O F T H E M U LT I VA R I AT E

DEPENDENCIES



As well as being multivariate in nature, usually in very high dimensions,

financial services firms’ risk variables may also exhibit directional

dependencies, or causal relationships. For example, high interest rates

may cause poor credit experience. On the other hand, it is not likely that

poor credit experience will cause high interest rates.

So, credit experience and interest rates are dependent and the direction

of the dependence is clear. In statistical parlance, we call credit experience a response variable and interest rate an explanatory variable.

In building a stochastic process to model these two risk variables, we

would normally work with the distribution of the response variable,

conditional on the explanatory variable, and with the marginal distribution of the explanatory variable itself.

Likewise, we expect government bond yields and equity dividend

yields to be dependent. These yields tend to take on high values together,

for example. However, there is no obvious causal relationship between

these variables. In statistical parlance both of these risk variables are

therefore response variables and we would therefore work with the full

bivariate distribution of these response variables in building a stochastic

process for these risk variables.

Deterministic stress testing should also acknowledge any directional

dependencies, or casual relationships, that may be present amongst

the risk variables. This can be achieved by developing conditional stress

tests for response variables, conditional on the values of the stressed



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